Question

Determine whether the sequence is arithmetic or geometric.

Sequence 1: –10, 20, – 40, 80, ...
Sequence 2: 15, – 5, – 25, – 45, ...
Which of the following statements are true regarding Sequence 1 and Sequence 2.

A) Sequence 2 is arithmetic and Sequence 1 is geometric.
B) Both sequences are arithmetic.
C) Both sequences are geometric.
D) Sequence 1 is arithmetic and Sequence 2 is geometric.

Answer 1

@iambatman

Answer 2

-.-

Answer 3

Haha, well there is a nice way to check this, lets look at the first sequence

\[-10, 20, -40, 80, ...\] do you see a pattern here?

Answer 4

yes I do.

Answer 5

Ok well lets look at the first two terms, -10, 20 notice if you multiply -10 by -2 you will get 20? Would the same work if you multiply 20 by -2 to get the next term (-40)?

Answer 6

Basically it's an arithmetic sequence if \[t_2-t_1 = t_3 - t_1\]and it's a geometric sequence if \[\frac{ t_2 }{ t_1 } = \frac{ t_3 }{ t_2 }\] that gives you your common ratio. Where the t represents the term, and the subscript is the address of the term, so \[t_1 = -10~~~t_2 = 20\] etc

Answer 7

an arithmetic sequence has the same difference between the terms and the geometric sequence has the same ratio between the terms.

Answer 8

in an arithmetic sequence, the next number is found by multiplying...and each term has to be multiplied by the same number.
In a geometric sequence, the next number is found by dividing...and each term has to be divided by the same number.